Truth Tables and Logical Connectives

[wanderingsun]

i've been trying to pass my finite math class for years - i am on my 4th attempt. i always screw up on the truth tables - i just couldn't get it.. you really helped me tremendously!! thank you! (haven't passed yet, but at least i am going to get past the damn truth tables!)

[missykim]

Oh boy, oh boy!  Discrete mathematics!!  I hope you make more of these videos :D  The concepts of Combination, Permutation, and Pigeon Hole Principle always kick my ass three ways from Sunday.  I mean, sure, I understand that if you have three pigeons and two holes, one of the holes it going to get two pigeons stuffed in there.  However, I'm never able to apply that to a problem.

[LeoGodin]

Your dinner/exercise example really helped me understand implies and bi-directional. Thanks.

[sjamil]

I'm in eight grade and I'm taking and algebra one class, I'm just watching your videos for the future and you explain very clearly! Subscribe!

[thingsnbits]

'Let's just say PatrickJMT has a large d... d-dinner'
LOL! 10/10

[fabrizzioorderique]

patrickJMT, thank you for your videos!! Could you make a folder/playlist containing all your videos on discrete math? I'm taking the course this semester and have found your videos to be super helpful. Thanks !

[matthewa]

Thanks, Patrick, very clear.

p=>q illustrates the necessary and sufficient distinction (that's how I think about it).

It is necessary that if Patrick has a large dinner, he will exercise the next morning (as he is trying to stay in shape and eating big dinners may make you overweight), however, it is not sufficient, as he may just not feel like it.

But I think that eating a big dinner isn't necessary or sufficient for exercising the next morning, and p doesn't imply q by necessity, so maybe this argument is fallacious.


I think a good example is thinking about the president of the US. As we know, all presidents must be born in the US.

What if the statement P is true and the statement Q is true? [1]

P: Obama was born in the US (is true)

Q: Obama was president of the US (is true)

Therefore, P implies Q.

What if the statement P is true and the statement Q is false? [2]

P: Obama was born in the US (is true)

Q: Obama was president of the US (is false)

Therefore, P does not imply Q.

Of couse we know that Obama became president, however, just because Obama was born in the US doesn't mean that this being true was sufficient for him becoming the president. Maybe the true Obama was born in the US and a fake Obama became president.

So, what if the statement P is false and the statement Q is true? [3]

P: Obama was born in the US (is false)

Q: Obama was president of the US (is true)

Therefore, P does not imply Q.

All people except “birthers” accept the statement P to be true. For them, it is a fallacy that Obama was allowed to be president, as they don’t think he was born in the US. For everybody else, the argument: Obama was born in the US and he was the president of the US is valid.

What if the statement P is false and the statement Q is false? [4]

P: Obama was born in the US (is false)

Q: Obama was president of the US (is false)

Therefore, not P implies not Q

Maybe the Obama wasn't born in the US, and hence he never became president.

However, the sane people know that only in case 1 are both truth values based on facts about the world (this captures the state of affairs in the world)— and remember that when making an argument, as long as its premise(s) are assumed to be true, then a valid conclusion can be derived, even though this argument may not be sound, i.e. BIRTHERS! (are you sure that the illuminati isn’t also spying on you?)


Um, WHAT’S WRONG WITH SOME PEOPLE!

So, I think this is an excellent case to think about this logical connective (implication).

[patricknshimiyimanaofficia]

I like the way you clarify things, stay ahead😊😊😊😊

[Lolorenzy]

More discrete math stuff soon please, I have a test on Friday lol

[kastro]

I love you man, I am from Saudi Arabia I like all of your's video and it helped me a lot .

[MrJ]

I feel the idea of implacation is incorrect. In the situation p -> q where p is false, both situations where q is true or false, the implication should be null. It seems like nonsense to says they are true.

[mollyc]

Implies : Think of this way. If someone is a liar, he could either lie to you, or tell you the truth.
But, if someone is an honest man, you can conclude that he wouldn't lie to you, but speak the truth.
Does that make sense to you?

[MrLostcause]

Thank you for help :)
e; I like that you use 0 and 1 instead of T and F because T and F really screws me up when looking at the table, I like the idea to use 0 and 1

[electronicsheep]

Hell yeah Truth Tables. Logic gates my favorite <3

[bryson]

This reminds me of logic gates for my digital electronics class. Is this a philosophy course?

[TASPlasma]

Will you be extending these videos as a Discrete Math type of thing, or a Philosophy type thing?

[WillhelmLiebniz]

The way I remember p implies q isn't true for p=false and q=true is because p didn't promise anything with its statement being that it is false. 
Example.  I am the king of England then you are the lord of welch.  I can't claim you as the lord of welch because I'm not the king of England. 

[zepe]

Wait so is he tells the moon is not made of cheese? Thats-

[Lolorenzy]

More discrete math stuff soon please, I have a test on Friday lol